An important factor affecting the classifier performance is the feature size. It is desired to minimize the feature size due to its effect on measurement cost and classifier accuracy. Both Principle Component Analysis (PCA) and Linear Discriminant Analysis (LDA) are statistical approaches for "Dimensionality Reduction" that are based on linear transformation, but are unsuitable for applications that are highly nonlinear functions of the original data. In this thesis, the effect of applying approximation methods on dimensionality reduction of feature space in pattern analysis is examined. The approximation methods are applied either in the signal domain or the transform domain. Mathematical analysis reduced the set of applicable methods to the Chebyshev polynomials, the Discrete Cosine Transform (DCT) and the Discrete Orthogonal polynomials. The present analysis excluded the Power series polynomials and Legender polynomials on grounds of violation of the orthogonality problem. A p1imitive dataset of images of leaves has been used to generate a bigger set of 5980 patterns of leave silhouettes falling into 4 different classes. Then this bigger set is reduced to 2589 patterns in order to balance between the set size, the size of the feature space and the computational time.

The generation of these patterns has been achieved by superimposing random white noise to the original silhouettes with levels varying between 10% and 40%. The original feature space for a given pattern was taken to be the radial signature of its boundary, and normalization procedure was formulated to achieve invariance under scale change, translation, rotation and change in the starting point. DCT, Chebyshev and Discrete Orthogonal polynomials successfully reduced about 85% of the dimensionality of feature space and in this region maximum classification results occurred; thus leading to saving in memory cost and running speed. DCT produced higher maximum classification rates using an Euclidean distance classifier, followed by the Chebyshev approximation method and the least classification rated are obtained by the Discrete Orthogonal polynomials. Maximum rates calculated were about 90%, 88% and 65% for the three approaches respectively. Moreover, and the more noise superimposed to the patterns the lower the classification rates obtained. Neural network classifiers results were about 10 -20% higher than the Euclidean distance classifier results, but however this is done in the expense of running time. Chebyshev polynomials produced the highest classification rates followed by DCT and then the Discrete Orthogonal Polynomials.


School of Sciences and Engineering


Computer Science & Engineering Department

Degree Name

MS in Computer Science

Date of Award


Online Submission Date


First Advisor

Amr Goneid

Committee Member 1

Ahmed Rafea

Committee Member 2

Amir Zeid

Committee Member 3

Abdel Badei Salem

Document Type



115 leaves

Library of Congress Subject Heading 1

Dimensional analysis


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Call Number

Thesis 2004/79



Included in

Engineering Commons